Republican presidential candidate Jeb Bush transitioned from defence to offence on Sunday after criticism from rival Donald Trump that his brother, former President George W. Bush, carried some blame for the September 11, 2001, attacks.

Mr Trump, the flamboyant front-runner in the 15-candidate Republican field, again provoked a tit-for-tat with Mr Bush on Friday by saying his brother must share some of the blame for the attacks that occurred during his first year in office.

“Look, my brother responded to a crisis, and he did it as you would hope a president would do,” Mr Bush said on CNN’s State of the Union.

“The great majority of Americans believe that. And I don’t know why he [Trump] keeps bringing this up.”

Mr Bush said Mr Trump’s comments about the September 11 attacks called his credibility into question. The former Florida governor attacked Mr Trump’s foreign policy credentials and compared his grip on international issues to a reality television show the billionaire businessman formerly hosted.

“Across the spectrum of foreign policy, Mr Trump talks about things that — as though he’s still on The Apprentice,” Mr Bush said.

Mr Trump doubled down on his comments during an appearance on Fox News Sunday, using a oft-repeated Jeb Bush phrase — that his brother “kept us safe” — against him.

“Jeb said: ‘We were safe with my brother. We were safe.’ Well the World Trade Centre just fell down,” Mr Trump said on the programme.